School of Mathematics and Statistics
The University of New South Wales
UNSW Sydney NSW 2052, Australia
email: cct@unsw.edu.au
Christopher C. Tisdell
Abstract:
This article examines the qualitative properties of solutions to systems of
boundary value problems involving fractional differential equations.
Our primary interest is in forming new results that involve sufficient
conditions for the existence of solutions. To do this, we formulate some
new ideas concerning a priori bounds on solutions, which are then
applied to produce the novel existence results.
The main techniques of the paper involve the introduction of novel
fractional differential inequalities and the application of the
fixed-point theorem of Schafer.
We conclude the work with several new results that link the number of
solutions to our problem with a fractional initial value problem,
akin to an abstract shooting method.
A YouTube video from the author that is designed to complement this
research is available at
youtube.com/watch?v=cDUrLsQLGvA
Submitted February 18, 2016. Published March 23, 2016.
Math Subject Classifications: 34A08.
Key Words: Existence of solutions; nonlinear fractional differential equations;
boundary value problem; Liapunov function; fixed point theorem.
Show me the PDF file (209 KB), TEX file, and other files for this article.
|
Christopher C. Tisdell School of Mathematics and Statistics The University of New South Wales UNSW Sydney NSW 2052, Australia email: cct@unsw.edu.au |
|---|
Return to the EJDE web page